The rate of rotation of a moving body about an axis may be determined by mounting an accelerometer on a frame and dithering it, with the accelerometer's sensitive axis and the direction of motion of the frame both normal to the rate axis about which rotation is to be measured. For example, consider a set of orthogonal axes X, Y and Z oriented with respect to the moving body. Periodic movement of the accelerometer along the Y axis of the moving body with its sensitive axis aligned with the Z axis results in the accelerometer experiencing a Coriolis acceleration directed along the Z axis as the moving body rotates about the X axis. A Coriolis acceleration is that perpendicular acceleration developed while the body is moving in a straight line, while the frame on which it is mounted rotates. This acceleration acting on the accelerometer is proportional to the velocity of the moving sensor body along the Y axis and its angular rate of rotation about the X axis. An output signal from the accelerometer thus includes a DC or slowly changing component or force signal F representing the linear acceleration of the body along the Z axis, and a periodic component or rotational signal .OMEGA. representing the Coriolis acceleration resulting from rotation of the body about the X axis.
The amplitude of that Coriolis component can be produced by vibrating the accelerometer, causing it to dither back and forth along a line perpendicular to the input axis of the accelerometer. Then, if the frame on which the accelerometer is mounted is rotating, the Coriolis acceleration component of the accelerometer's output signal will be increased proportionally to the dither velocity. If the dither amplitude and frequency are held constant, then the Coriolis acceleration is proportional to the rotation rate of the frame.
The linear acceleration component and the rotational component representing the Coriolis acceleration may be readily separated by using two accelerometers mounted in back-to-back relationship to each other and processing their output signals by sum and difference techniques. In U.S. Pat. No. 4,510,802, assigned to the assignee of this invention, two accelerometers are mounted upon a parallelogram with their input axes pointing in opposite directions. An electromagnetic D'Arsonval coil is mounted on one side of the parallelogram structure and is energized with a periodically varying current to vibrate the accelerometers back and forth in a direction substantially normal to their sensitive or input axis. The coil causes the parallelogram structure to vibrate, dithering the accelerometers back and forth. By taking the difference between the two accelerometer outputs, the linear components of acceleration are summed. By taking the sum of the two outputs, the linear components cancel and only the Coriolis or rotational components remain.
U.S. Pat. No. 4,509,801, commonly assigned to the assignee of this invention, describes the processing of the output signals of two accelerometers mounted for periodic, dithering motion to obtain the rotational rate signal .OMEGA. and the force or acceleration signal F representing the change in velocity, i.e. acceleration of the moving body, along the Z axis. U.S. Pat. No. 4,510,802, commonly assigned to the assignee of this invention, describes a control pulse generator, which generates and applies a sinusoidal signal of a frequency .omega. to the D'Arsonval coil to vibrate the parallelogram structure and thus the first and second accelerometer structures mounted thereon, with a dithering motion of the same frequency .omega.. The accelerometer output signals are applied to a processing circuit, which sums the accelerometer output signals to reinforce the linear components indicative of acceleration. The linear components are integrated over the time period T of the frequency .omega. corresponding to the dither frequency to provide the force signal F, which represents the change in velocity, i.e. acceleration, along the Z axis. The accelerometer output signals are also summed, whereby their linear components cancel and their Coriolis components are reinforced to provide a signal indicative of frame rotation. That difference signal is multiplied by a zero mean periodic function sync .omega.t. The resulting signal is integrated over a period T of the frequency .omega. by a sample and hold circuit to provide the signal .OMEGA. representing the rate of rotation of the frame.
The D'Arsonval coil is driven by a sinusoidal signal of the same frequency .omega. which corresponded to the period T in which the linear acceleration and Coriolis component signals were integrated. In particular, the pulse generator applies a series of pulses at the frequency .omega. to a sine wave generator, which produces the substantially sinusoidal voltage signal to be applied to the D'Arsonval coil. A pair of pick-off coils produce a feedback signal indicative of the motion imparted to the accelerometers. That feedback signal is summed with the input sinusoidal voltage by a summing junction, whose output is applied to a high gain amplifier. The output of that amplifier in turn is applied to the D'Arsonval type drive coil. The torque output of the D'Arsonval coil interacts with the dynamics of the parallelogram structure to produce the vibrating or dither motion. In accordance with well known servo theory, the gain of the amplifier is set high so that the voltage applied to the summing junction and the feedback voltage are forced to be substantially equal and the motion of the mechanism will substantially follow the drive voltage applied to the summing junction.
U.S. Pat. No. 4,881,408 describes the use of vibrating beam force transducers in accelerometers. In U.S. Pat. No. 4,372,173, the force transducer takes the form of a double-ended tuning fork fabricated from crystalline quartz. The transducer comprises a pair of side-by-side beams which are connected to common mounting structures at their ends. Electrodes are deposited on the beams and a drive circuit applies a periodic voltage signal to the electrodes causing the beams to vibrate toward and away from one another, 180 degrees out of phase. In effect, the drive circuit and beams form an oscillator with the beams playing the role of a frequency controlled crystal, i.e., the mechanical resonance of the beams controls the oscillation frequency. The vibrating beams are made of crystalline quartz, which has piezoelectric properties. Application of periodic drive voltages to such beams cause them to vibrate toward and away from one another, 180 degrees out of phase. When the beams are subjected to accelerating forces, the frequency of the mechanical resonance of the beams changes, which results in a corresponding change in the frequency of the drive signal. When subjected to acceleration forces that cause the beams to be placed in tension, the resonance frequency of the beams and thus the frequency of the drive signal increases. Conversely, if the beams are placed in a compression by the acceleration forces, the resonance frequency of the beams and the frequency of the drive signal is decreased.
Above referenced U.S. Pat. No. 5,005,413 describes accelerometers using vibrating force transducers that use materials with low internal damping, to achieve high Q values that result in low drive power, low self-heating and insensitivity to electronic component variations. Transducer materials for high-accuracy instruments also require extreme mechanical stability over extended cycles at high stress levels. Crystalline silicon possesses high Q values, and with the advent of low cost, micromachined mechanical structures fabricated from crystalline silicon, it is practical and desirable to create vibrating beams from a silicon substrate. Commonly assigned U.S. Pat. No. 4,912,990 describes a vibrating beam structure fabricated from crystalline silicon and including an electric circuit for applying a drive signal or current along a current path that extends in a first direction along a first beam and in a second, opposite direction along a second beam parallel to the first. A magnetic field is generated that intersects substantially perpendicular the conductive path, whereby the first and second beams are caused to vibrate towards and away from one another, 180 degrees out of phase.
Digital techniques employ stable, high frequency crystal clocks to measure a frequency change as an indication of acceleration forces applied to such vibrating beam accelerometers. To ensure precise integration or cosine demodulation, a crystal clock is used to set precisely the frequency of the dither drive signal. Outputs from two accelerometers are fed into counters to be compared to a reference clock signal produced by the crystal clock. A microprocessor reads the counters and processes the data to provide a force signal F and a rotational signal .OMEGA.. The main advantage of digital processing is the ability to demodulate with extreme precision. The short term stability of the reference crystal clock allows the half-cycle time basis to be precisely equal. Thus a constant input to the cosine demodulator is chopped up into equal, positive half-cycle and negative half cycle values, whose sum is exactly zero.
In an illustrative embodiment, the two accelerometer signals are counted in their respective counters over 100 Hz period, which corresponds to a 100 Hz of the dither frequency .omega., and are sampled at a 400 Hz data rate corresponding to each quarter-cycle of the dither motion. The two accumulated counts are subtracted to form the force signal F. Since the counters act as an integrator, the acceleration signal is changed directly to a velocity signal. Taking the difference of the acceleration signals tends to reject all Coriolis signals as does the counter integration and locked period data sampling.
The Coriolis signals are detected by a cosine demodulation. The cosine demodulated signals from the first and second accelerometers are summed to produce the .DELTA..theta. signal. Again, the counters integrate the rate data to produce an angle change. The sum also eliminates any linear acceleration and the demodulation cancels any bias source including bias operating frequency and accelerometer bias. The accelerometer temperature is used in a polynomial model to provide compensation for all the coefficients used to convert the frequency counts into output units. Thus, the scale factor, bias and misalignment of the sensor axes are corrected over the entire temperature range.
The demodulation of the frequency sample is straightforward once the data is gathered each quarter-cycle. The cosine demodulation is simply the difference between the appropriate half-cycles. The linear acceleration is the sum of all samples.
Various issues with the use of vibrating beam force transducers in accelerometers include the need to operate the device in a substantial vacuum such that the beams can vibrate at their natural frequency without loss of energy from viscous damping. Also, the vibrating beams of the first and second accelerometers are formed in first and second layers of epitaxial material formed on opposing sides of the silicon substrate so that the force sensing axis of each accelerometer is directed opposite to the direction of the other. In other words, the vibrating beams must be on opposing sides of the substrate so that one will be in compression and the other in tension when subjected to an applied acceleration force. The high doping levels in the epitaxial layer required to form the vibrating beams make the material inherently unstable. Thus, the output of the vibrating beams tends to degrade over time and with exposure to thermal environments. The nature of vibrating beam transducers causes accelerometer design and analysis to be relatively complex as compared to that of simpler force rebalance accelerometers and their larger size reduces the quantity of accelerometers which can be fabricated in a single wafer of silicon substrate so that vibrating beam accelerometers are inherently more expensive to produce than miniature force rebalance accelerometers.
Miniature silicon force-rebalance accelerometers in an integrated circuit form are small and inexpensive and generally have a large dynamic range and are operable in high vibration environments over a wide temperature range. Miniature silicon force-rebalance accelerometers having a silicon proof mass suspended between a pair of electrode layers and responsive to differential capacitive coupling between the electrode layers and the proof mass for opposing acceleration forces applied to the proof mass are described in above incorporated U.S. Pat. No. 4,336,718. The miniature silicon force-rebalance accelerometer of the prior art includes a proof mass and two flexures integrally formed from a silicon substrate. The flexure preferably defines a bend line along the mid-plane of the proof mass which is intended to minimize vibration rectification. The silicon substrate including the proof mass is anodically bonded between upper and lower glass substrates having upper and lower metal, for example, gold, electrodes deposited thereon. The upper and lower substrates are preferably formed identically. Symmetry between opposing surfaces of the proof mass and between opposing the electrodes deposited on the upper and lower glass substrates surfaces minimizes bias and maximizes dynamic range and linearity.
The accelerometer balances applied acceleration forces by applying electrical restoring forces to the proof mass through the electrodes of the upper and lower substrates. Parallel AC and DC signals are applied to the proof mass. Capacitances formed between the electrodes on each of the upper and lower substrates and the proof mass are coupled to a differential bridge circuit. The output of the differential bridge filter is used to drive the electrodes of the upper and lower substrates. An acceleration output of the differential bridge filter is applied to the electrodes of the upper and lower substrates to apply electrostatic restoring forces to the proof mass thereby balancing the applied acceleration forces. The magnitude of the restoring force required to restore the proof mass to a neutral position between the opposing upper and lower substrates is a function of the applied acceleration force and is measured to determine the acceleration field.
The miniature silicon force-rebalance accelerometer of the prior art also include additional electrodes on the upper and lower substrates which are substantially thicker than the electrodes through which the electrical restoring forces are applied to the proof mass. These so called "guard band" electrodes cause the proof mass to stand-off from the upper and lower electrodes when the accelerometer is not in servo. The upper and lower guard band electrodes are held at the same potential as the proof mass. The gaps on the upper and lower substrates between the restoring electrodes and the guard electrodes is necessarily small such that the potential difference between the restoring and guard band electrodes causes current leakage across the gap and the substrate material therebetween becomes charged. The potential in the gaps acts as an extension of the potential of the upper and lower restoring electrodes which is indistinguishable from the applied restoring force and, thus, negatively impacts performance. The prior art device attempts to partially mitigate this impact on performance by minimizing the size of the guard electrodes relative the upper and lower restoring electrodes and cutting a groove in the proof mass surface opposite the gaps so that the influence of the potential in the gaps is less significant. Alternatively, the upper and lower substrates, particularly in the gaps between the restoring electrodes and the guard electrodes, are coated with a thin, slightly conductive material to quickly establish and hold essentially constant the potential distribution in the gap.
Outer surfaces of the upper and lower substrates opposite the restoring and guard band electrodes are metalized and grounded shield the transducer from outside electrical fields. Metallic bond pads are formed on the surface of the proof mass and wire bonds provide electrical contacts with the sensor circuitry in one of several manners common to the integrated circuit industry. During operation, an applied acceleration causes relative motion between the proof mass and the upper and lower electrodes as the proof mass attempts to pivot about the two suspension flexures. An imbalance in capacitances between the proof mass and the upper and lower electrodes results which the sensor circuitry balances by applying an electromotive force to the proof mass through the restoring electrodes to move the proof mass to a neutral position between the upper and lower electrodes and hold it there. For example, as the proof mass moves and approaches one of the electrodes and recedes from the other, an increased capacitive pickup of the AC signal causes the differential bridge circuit to apply an increased DC signal voltage to the approaching electrode and to decrease the signal voltage applied to the receding electrode which serves to apply an electrostatic force to the proof mass to resist the force of acceleration and restore the proof mass to a neutral position.
The state of the art in micromachined rate and acceleration sensors is represented by U.S. Pat. No. 5,341,682 which is commonly assigned to the assignee of the present invention and incorporated herein by reference. The rate of rotation of a moving body about an axis may be determined by mounting an accelerometer on a frame and dithering it, with the accelerometer's sensitive axis and the direction of motion of the frame both normal to the rate axis about which rotation is to be measured. A Coriolis acceleration is the measure of the acceleration developed while the body is moving in a straight line and the frame upon which it is mounted rotates about the rate axis. The amplitude of the Coriolis component can be produced by vibrating or dithering the accelerometer, causing it to dither back and forth along a line perpendicular to the input axis of the accelerometer. When the frame upon which the accelerometer is mounted is rotated, the Coriolis acceleration component of the accelerometer's output signal increases in proportion to the dither velocity.
The linear acceleration component and the rotational component representing the Coriolis acceleration may be readily separated by using two accelerometers mounted in back-to-back relationship to each other and processing their output signals by sum and difference techniques as described in U.S. Pat. No. 4,590,801, which is commonly assigned to the assignee of the present invention and incorporated herein by reference.
Rate and acceleration sensors, for example, U.S. Pat. No. 5,341,682, are comprised of two accelerometers aligned in a single plane such that the input or sensitive axes of the two accelerometers are parallel and the output or hinge axes of the two accelerometers are parallel. The two accelerometers are vibrated or dithered at a predetermined frequency along a dither axis parallel to the hinge axes. The two accelerometers tend to vibrate at slightly different frequencies due to slight mass mismatch. Even if driven by a drive signal of common frequency, the accelerometer motions tend to be out of phase with each other. A link is connected to each of the two accelerometers whereby motion imparted to one accelerometer results in like but opposite motion imparted to the other accelerometer. Thus, the dithering motion imparted to one accelerometer is ideally of the exact same frequency and precisely 180 degrees out of phase with that applied to the other accelerometer.
The link provides an interconnect between the two accelerometers which is stiff in the dither axis such that the motion imparted to one accelerometer is effectively transmitted to the other accelerometer and both accelerometers ideally dither at the same frequency and precisely 180 degrees out of phase. The link is pivotally fixed to the frame by a pivot flexure. The link is further connected to each of the two accelerometers by flexures. The link is formed in a complex asymmetric shape. The complexity of the link is driven by practical considerations involved in adapting the link to accommodate both the pivot flexure and the two link-to-accelerometer flexures. The link's complex asymmetric shape provides adequate clearance between the link and the frame for the pivot flexure. The link's shape also provides adequate clearance between the link and each accelerometer to provide the precise flexure length to ensure that the flexures exhibit a predetermined mix of simple arc bending and "S-bend" motion and to ensure that any motion imparted to one accelerometer by the flexures is imparted to the other accelerometer as a sinusoidal function without introducing a higher order harmonic into the translation motion.
Although the complex asymmetric link described in U.S. Pat. No. 5,341,682 functions for the purposes intended, its exact behavior is difficult to predict and/or model analytically. For example, the complex shape of the link results in spring rates which are asymmetrical and a shape which is difficult to solve analytically. Additionally, constructing the shape previously taught results in flexures whose thicknesses and hence vibration properties are difficult to control. Therefore, later patent applications, for example, above incorporated U.S. application Ser. No. 09/016,186 and similarly incorporated U.S. application Ser. No. 09/134,810, provide links having simple geometric shapes formed symmetrically about the pivot point. The behavior of these simpler symmetric links is more easily predicted and/or modeled analytically. For example, these simpler symmetric links result in spring rates which are symmetrical and easier to solve analytically using conventional methods. Additionally, constructing the simpler symmetric shape results in flexures whose thicknesses and hence vibration properties are more easily controlled.